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Publishing Venue

IBM

Abstract

Robot with non-deterministic characteristics
Given a robot with a positioning interface including smooth braking to its final position and no feedback to the positioning interface, this article describes a method for moving the robot in a time predictable manner. Generally a robot with smooth braking is given a target position and accelerates the required motors (up to a maximum) to achieve this position and then decelerates continuously until the desired position is reached. The motor speed and the time to reach any point is therefore dependent on the distance between the start and end points and load on the robot.
Feedback within the robot circuitry makes arrival time unpredictable. Figure 1 shows an ideal speed curve for smoothly arriving at a desired position.
Figure 1. Ideal speed curve

Country

United States

Language

English (United States)

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Given a robot with a positioning interface including smooth braking to its final position and no feedback to the positioning interface, this article describes a method for moving the robot in a time predictable manner. Generally a robot with smooth braking is given a target position and accelerates the required motors (up to a maximum) to achieve this position and then decelerates continuously until the desired position is reached. The motor speed and the time to reach any point is therefore dependent on the distance between the start and end points and load on the robot.

Feedback within the robot circuitry makes arrival time unpredictable. Figure 1 shows an ideal speed curve for smoothly arriving at a desired position.

Figure 1. Ideal speed curve

There is a short ramp up to maximum speed and a uniform ramp down to the final position. Unfortunately, a typical speed curve looks like the one shown if Figure 2.

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Figure 2. Actual possible speed curve

Although the ramp up remains consistent, the ramp down can be riddled with extra motor adjustments to push the robot into the final position. Because of the unpredictable nature of this positioning, the ramp down must be minimized when positioning in real-time. The approach is to remove the unpredictable parts of the curve.

Finally, Figure 3 shows a speed curve resulting when a short movement is required where the maximum speed is not reached before the ramp down is imposed.

Figure 3. Short distance speed curve

Here the ideal ramp down is shown although an unpredictable ramp down is possible as well.

Making the positioning deterministic

Given that the robot has boundaries where travel is impossible, the solution involves a finite set of positioning values where predictable movement can be achieved. Within the finite set, the motors are

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accelerated to maximum speed and stopped abruptly at the desired position. This is achieved by sending a position signal which instructs the robot to go to the boundary in the direction of the desired position, waiting a computed amount of time based on distance and load, and then sending the desired position causing the robot to brake at the position. The computed time matches the distance travelled over that time allowing for little or no drift into the desired position. This means that there is a required minimum time of arrival per distance (since the robot ca...